ergo
template_lapack_lae2.h
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1 /* Ergo, version 3.8, a program for linear scaling electronic structure
2  * calculations.
3  * Copyright (C) 2019 Elias Rudberg, Emanuel H. Rubensson, Pawel Salek,
4  * and Anastasia Kruchinina.
5  *
6  * This program is free software: you can redistribute it and/or modify
7  * it under the terms of the GNU General Public License as published by
8  * the Free Software Foundation, either version 3 of the License, or
9  * (at your option) any later version.
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13  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14  * GNU General Public License for more details.
15  *
16  * You should have received a copy of the GNU General Public License
17  * along with this program. If not, see <http://www.gnu.org/licenses/>.
18  *
19  * Primary academic reference:
20  * Ergo: An open-source program for linear-scaling electronic structure
21  * calculations,
22  * Elias Rudberg, Emanuel H. Rubensson, Pawel Salek, and Anastasia
23  * Kruchinina,
24  * SoftwareX 7, 107 (2018),
25  * <http://dx.doi.org/10.1016/j.softx.2018.03.005>
26  *
27  * For further information about Ergo, see <http://www.ergoscf.org>.
28  */
29 
30  /* This file belongs to the template_lapack part of the Ergo source
31  * code. The source files in the template_lapack directory are modified
32  * versions of files originally distributed as CLAPACK, see the
33  * Copyright/license notice in the file template_lapack/COPYING.
34  */
35 
36 
37 #ifndef TEMPLATE_LAPACK_LAE2_HEADER
38 #define TEMPLATE_LAPACK_LAE2_HEADER
39 
40 
41 template<class Treal>
42 int template_lapack_lae2(const Treal *a, const Treal *b, const Treal *c__,
43  Treal *rt1, Treal *rt2)
44 {
45 /* -- LAPACK auxiliary routine (version 3.0) --
46  Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
47  Courant Institute, Argonne National Lab, and Rice University
48  October 31, 1992
49 
50 
51  Purpose
52  =======
53 
54  DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix
55  [ A B ]
56  [ B C ].
57  On return, RT1 is the eigenvalue of larger absolute value, and RT2
58  is the eigenvalue of smaller absolute value.
59 
60  Arguments
61  =========
62 
63  A (input) DOUBLE PRECISION
64  The (1,1) element of the 2-by-2 matrix.
65 
66  B (input) DOUBLE PRECISION
67  The (1,2) and (2,1) elements of the 2-by-2 matrix.
68 
69  C (input) DOUBLE PRECISION
70  The (2,2) element of the 2-by-2 matrix.
71 
72  RT1 (output) DOUBLE PRECISION
73  The eigenvalue of larger absolute value.
74 
75  RT2 (output) DOUBLE PRECISION
76  The eigenvalue of smaller absolute value.
77 
78  Further Details
79  ===============
80 
81  RT1 is accurate to a few ulps barring over/underflow.
82 
83  RT2 may be inaccurate if there is massive cancellation in the
84  determinant A*C-B*B; higher precision or correctly rounded or
85  correctly truncated arithmetic would be needed to compute RT2
86  accurately in all cases.
87 
88  Overflow is possible only if RT1 is within a factor of 5 of overflow.
89  Underflow is harmless if the input data is 0 or exceeds
90  underflow_threshold / macheps.
91 
92  =====================================================================
93 
94 
95  Compute the eigenvalues */
96  /* System generated locals */
97  Treal d__1;
98  /* Local variables */
99  Treal acmn, acmx, ab, df, tb, sm, rt, adf;
100 
101 
102  sm = *a + *c__;
103  df = *a - *c__;
104  adf = absMACRO(df);
105  tb = *b + *b;
106  ab = absMACRO(tb);
107  if (absMACRO(*a) > absMACRO(*c__)) {
108  acmx = *a;
109  acmn = *c__;
110  } else {
111  acmx = *c__;
112  acmn = *a;
113  }
114  if (adf > ab) {
115 /* Computing 2nd power */
116  d__1 = ab / adf;
117  rt = adf * template_blas_sqrt(d__1 * d__1 + 1.);
118  } else if (adf < ab) {
119 /* Computing 2nd power */
120  d__1 = adf / ab;
121  rt = ab * template_blas_sqrt(d__1 * d__1 + 1.);
122  } else {
123 
124 /* Includes case AB=ADF=0 */
125 
126  rt = ab * template_blas_sqrt(2.);
127  }
128  if (sm < 0.) {
129  *rt1 = (sm - rt) * .5;
130 
131 /* Order of execution important.
132  To get fully accurate smaller eigenvalue,
133  next line needs to be executed in higher precision. */
134 
135  *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b;
136  } else if (sm > 0.) {
137  *rt1 = (sm + rt) * .5;
138 
139 /* Order of execution important.
140  To get fully accurate smaller eigenvalue,
141  next line needs to be executed in higher precision. */
142 
143  *rt2 = acmx / *rt1 * acmn - *b / *rt1 * *b;
144  } else {
145 
146 /* Includes case RT1 = RT2 = 0 */
147 
148  *rt1 = rt * .5;
149  *rt2 = rt * -.5;
150  }
151  return 0;
152 
153 /* End of DLAE2 */
154 
155 } /* dlae2_ */
156 
157 #endif
template_blas_sqrt
Treal template_blas_sqrt(Treal x)
absMACRO
#define absMACRO(x)
Definition: template_blas_common.h:47
template_lapack_lae2
int template_lapack_lae2(const Treal *a, const Treal *b, const Treal *c__, Treal *rt1, Treal *rt2)
Definition: template_lapack_lae2.h:42